# Moderate Alligations or Mixtures Solved QuestionAptitude Discussion

 Q. A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. What part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
 ✖ A. 7/11 ✖ B. 6/7 ✔ C. 1/5 ✖ D. 2/7

Solution:
Option(C) is correct

Suppose the vessel initially contains 8 litres of liquid.

Let $x$ litres of this liquid be replaced with water then quantity of water in new mixture

$=3-\dfrac{3x}{8}+x$ litres

Quantity of syrup in new mixture $=5-\dfrac{5x}{8}$ litres

After replacement, the quantity of water and syrup is same in the new mixture.

Therefore,

\begin{align*}
3-\dfrac{3x}{8}+x &= 5-\dfrac{5x}{8}\\
\Rightarrow 5x+24 &=40-5x\\
\Rightarrow 10x &=16\\
\Rightarrow x &=\dfrac{8}{5}
\end{align*}

So part of the mixture replaced,

$=\dfrac{8}{5}\times \dfrac{1}{8} = \dfrac{1}{5}$

## (6) Comment(s)

Chakarya
()

Syrup part is only getting added with water mixture. So,

3/8 + 5x/8 = 1/2

(Water in mix + Syrup getting added with water) = Half of water or syrup

Solving for x, we get x = 1/5

Kritarth
()

why the answer 8/5 has been multiplied with 1/8 ? please explain...thank u

Smart
()

8 by 5 litre mixure out of 8 litre initial solution is replaced that is 1 by 5 part of initial mixture

Div
()

Parul
()

plzz explain it...

Sim
()

not getting it........